Nick Clegg has endorsed the government's decision to ask the Guardian to destroy leaked secret NSA documents on the grounds that Britain would face a "serious threat to national security" if they reached the "wrong hands".

In a statement, a spokesman for the deputy prime minister gave the first official confirmation that the cabinet secretary, Sir Jeremy Heywood, made the request to the Guardian.

The intervention by Clegg came after Yvette Cooper said that parliament's intelligence watchdog should investigate David Cameron's role in asking the Guardian to surrender or destroy the NSA documents. The shadow home secretary made her call after the Daily Mail and the Independent reported that Heywood made the request to the Guardian on the instructions of the prime minister.

Keith Vaz, the Labour chairman of the Commons home affairs select committee, said that the prime minister must make a statement to MPs when parliament returns next month.

In a statement issued after the official confirmation that Heywood asked the Guardian to delete its hard drives, Vaz said: "The actions of the cabinet secretary are unprecedented and show that this issue has reached the highest levels of government. Although I am very surprised at this revelation it explains why Downing Street, the White House and the home secretary were briefed in advance about David Miranda's detention.

"Up until now the UK government has downplayed its interest in these matters but it's clear that they have taken a proactive stance not just in terms of the destruction of the information held by the Guardian but also the involvement of those journalists who have written about Edward Snowden. The prime minister must make a full statement to parliament on the day it returns. We need to know the full facts nothing less will do."

A spokesman for Clegg made clear that Heywood was acting on the authority of both the prime minister and his deputy. The spokesman said: "We understand the concerns about recent events, particularly around issues of freedom of the press and civil liberties. The independent reviewer of terrorism legislation is already looking into the circumstances around the detention of David Miranda and we will wait to see his findings.

"On the specific issue of records held by the Guardian, the deputy prime minister thought it was reasonable for the cabinet secretary to request that the Guardian destroyed data that would represent a serious threat to national security if it was to fall into the wrong hands.

"The deputy prime minister felt this was a preferable approach to taking legal action. He was keen to protect the Guardian's freedom to publish, whilst taking the necessary steps to safeguard security.

"It was agreed to on the understanding that the purpose of the destruction of the material would not impinge on the Guardian's ability to publish articles about the issue, but would help as a precautionary measure to protect lives and security."

Clegg clarified the government's position after Labour sought to focus attention on the prime minister's role in instructing Heywood. Cooper told the Today programme on Radio 4: "We don't know what was on the [hard drives] or what the material was that the government was pursuing. Clearly the government does have a responsibility to protect national security. However, I think this may be another area where an inquiry by the intelligence and security committee may be the right way forward in terms of this particular case and what the prime minister's role was."

Alan Rusbridger, the editor of the Guardian, had disclosed on Monday night that a "very senior government official claiming to represent the views of the prime minister" asked him to return or destroy all the NSA documents leaked to the paper.

The Guardian agreed to destroy two hard drives last month in the presence of two security experts from Britain's GCHQ eavesdropping centre after the government threatened to take legal action.

Rusbridger told officials that the Guardian would continue to report from the leaked documents because it had backup copies in the US and in Brazil. Glenn Greenwald, the Guardian journalist who received the documents from the US whistleblower Edward Snowden, lives in Rio de Janeiro.

In her BBC interview, Cooper suggested that the government may have acted in an evasive manner after the nine-hour detention of David Miranda, Greenwald's partner, at Heathrow airport on Sunday. Miranda was detained under anti-terror laws as he flew home to Rio from Berlin via London.

During his trip to Berlin, Miranda met Laura Poitras, the US film-maker who has been working with Greenwald and the Guardian. Officials confiscated Miranda's mobile phone, laptop, camera, memory sticks, DVDs and games consoles.

Cooper said: "I have two concerns about this case. The first is whether or not it was appropriate or legally justified to use terrorism powers in this case when there were other legal avenues that could have been pursued. The second was whether the home secretary and the government have been evasive about their role in this process, which has rather had to be dragged out of them. We still don't know the full position."

The shadow home secretary questioned the use of schedule 7 of the Terrorism Act 2000 to detain Miranda after Lord Falconer of Thoroton, the former lord chancellor, said there was no legal basis under the act to hold him. Falconer told the Guardian that police had the right to detain anyone, even when they do not suspect them of terrorism. But they have to assess whether the person has been involved in the commission, preparation or instigation of terrorism. "Plainly Mr Miranda is not such a person," Falconer said.

Sir Malcolm Rifkind, the former foreign secretary who chairs the ISC, said the use of anti-terror laws to detain Miranda was a "sensitive issue" that should be investigated. But he told the Today programme: "This was not about embarrassment to the government. The documents which Snowden stole from the National Security Agency are documents some of which deal with how the intelligence agencies get access to terrorist information through interception of mail or phone messages. That is something potentially relevant to terrorists and therefore it is not a question of embarrassment to the government."

Rifkind was strongly supportive of the way in which the government sought the return or destruction of the leaked NSA documents. "I think Mr Rusbridger, in the article he wrote about the destruction of his hard disks, is on relatively weak ground. He clearly did not dispute that he had no legal right to possess the files or the documents. The question was whether he handed them back to the government or whether they were destroyed. He chose the latter option.

"Clearly if he thought that what he was doing was perfectly lawful, that he was perfectly entitled to have these documents, he would have told the cabinet secretary – or whoever it was – to go and get lost and take me to court. But he didn't do that. He knew perfectly well that if you have in your possession documents which were originally stolen you are on pretty dodgy ground."